All that it takes to be saved is, to believe on the Lord Jesus. Believe in your heart and say or call upon the name of the Lord, as Saul of Tarsus did when Jesus appeared to him on the road to Damascus, and you will be saved. All that Paul said in repentance was "Lord!" When Jesus confronted him saying "Why do you persecute ME!?" Saul could have remembered hearing what his mentor Gamaliel said, Do not prevent them or you may find yourself to be against God."
Acts 2:37-39
When the Jewish from nations round about heard this, they were cut to their hearts and asked Peter and the other apostles, “Brothers, what shall we do?”
Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. This promise belongs to you and your children and to all who are far off—to all whom the Lord our God will call to Himself.”
* The gentiles in Acts 10 Peter said We are witnesses of all that He did, both in the land of the Jews and in Jerusalem. And although they put Him to death by hanging Him on a tree, God raised Him up on the third day and caused Him to be seen— not by all the people, but by the witnesses God had chosen beforehand, by us who ate and drank with Him after He rose from the dead. And He commanded us to preach to the people and to testify that He is the One appointed by God to judge the living and the dead. All the prophets testify about Him that everyone who believes in Him receives forgiveness of sins through His name.”
Peter had not said anything to them about repentance .. when .. "the Holy Spirit fell upon all who heard his message".
Peter was interrupted by the Holy Spirit.. the gentiles didn't say any words unto salvation, but they believed in their heart and God poured out His Spirit upon them. They skipped saying any words unto salvation, no words of repentance for sins or anything, they went right to being baptized in the Spirit and speaking in tongues.
* The thief on the cross said no salvation formula whatsoever, all he said to Jesus was.. "Remember me when you come into your kingdom." And Jesus said to him "Today you will be with me in paradise." The thief was as good as saved just by his own words.
Yes, you can be saved by a prayer of your own, or by the given salvation prayer of another for you to repeat after.. even though you know little or not much at all about how to be saved, even though you know little about theological topics such as Jesus being raised from the dead. When you believe in Jesus to save you, you are by definition believing that He is alive to hear you and thereby save you.
There is a scripture that says Believe on the Lord Jesus and you and your household shall be saved. Paul used the same principle to ensure that all in the ship with him would live and none die because of the storm at sea.
The Bible does not make salvation complicated that you have to use a certain formula of words to be saved or that you have to hear a sermon and understand all of the theological connecting topics of redemption and salvation in order to be saved.
Jesus did all of the complicated work for us when he was on the cross in our place in order for salvation to be easy for us.
It's not magic. It's faith. All you have to do is believe.